He said it would be wrong to let changes in the EU "unfold naturally" without Britain having a role in shaping reform and seeking fresh consent from its citizens.

At the moment, Europe is being "out-competed and out-invested" by emerging markets, he said.

"It's time we make it an engine for growth, not a source of cost for business and complaint for our citizens," he said. "I want the UK to look out, not in."

He spoke in at the business summit in Switzerland just minutes after Nick Clegg, the deputy Prime Minister, called his plans to claw back powers and hold a public vote "wholly implausible".

Speaking on his weekly LBC radio show, Liberal Democrat leader said the UK risks "tying itself in knots" as it tries to do a deal that would "benefit us and disadvantage everybody else" .

However, the Germans, Czechs, Dutch and Finnish have so far suggested it could be possible for Britain to get a new relationship with Brussels.

Angela Merkel, the German Chancellor, said she is prepared to listen to Britain's "wishes" about the EU and would like to see a "fair compromise".

This morning, Alexander Stubb, Finland's foreign affairs minister, also said he thought the speech was "gutsy" and "constructive".

The staunch pro-European told BBC Radio Four's Today programme that it ought to be perfectly possible for Britain to "differentiate" itself in Europe as lots of countries have previously taken "a few raisins out of the bun".

Mr Cameron has not yet set out which powers he would like to get back from the EU. But last night, David Lidington, the Europe minister, said the Conservative manifesto would set out more detail on Britain's approach to re-balancing its links with Brussels.

Chris Grayling, the Justice Secretary, told BBC Breakfast this morning that the Prime Minister would not "start with a detailed list of items" but he would look at areas such as justice, employment rights and the environment.

The Prime Minister's landmark speech on Wednesday said it is "time for the British people to have their say" amid growing public discontent about the power of Brussels.

He pledged an in-out referendum in the first half of the next parliament, arguing that democratic consent for membership is currently "wafer thin".

"It is time to settle this European question in British politics," he said. "I say to the British people: this will be your decision."

His promise to hold a poll was greeted with relief and praise from a wide range of Conservative MPs, but the reception across the Channel has proved mixed.

Guido Westerwelle, Germany's foreign minister said he "wants the United Kingdom to remain an active and constructive part of the European Union" but insisted "cherry-picking is not an option."

One French foreign minister, Laurent Fabius, also told France Info radio that the EU would be happy to "roll out the red carpet" for departing businesses from Britain if it really wants to go.

"It risks being dangerous for Britain itself because Britain outside of Europe, that will be difficult," he said.

"We can't have Europe a la carte. Imagine the EU was a football club: once you've joined up and you're in this club, you can't then say you want to play rugby.

"The other day I had a meeting with British businessmen and I told them: Listen, if Britain decides to leave Europe, we will roll out the red carpet for you."

After the speech, Mr Cameron acknowledged there would be difficult negotiations and some would view his attitude to reform as "heretical".

However, the Prime Minister has long been battling demands from within his party for an immediate referendum. Several Cabinet ministers privately believe that Britain should consider leaving the EU.

The tone of his speech appeared to have won round many of the most Eurosceptic Tories and even pressure groups such as OpenEurope.

Boris Johnson, the London Mayor, described the speech as "bang on", while Lord Lamont, the former Chancellor, called it an "excellent" performance that will "appeal not just to the Conservative party but to a very large section of the British people who are uneasy about our position in Europe".

Bernard Jenkin, a Tory MP and executive member of the backbench 1922 committee, welcomed the "very profound" that will recast the UK's relationship with Europe.

"It's a watershed speech," he said. "It is a commitment to give the British people a say, which all political parties at some time have intimated they would do but we've never quite got there have we? But this is a very very big moment in British politics."

The promise of a referendum may help the Conservatives win back votes lost to Ukip, the eurosceptic party, which has seen record support in recent months.

Nigel Farage, the Ukip leader, said he is happy that the EU issue has become part of mainstream debate but his party will continue to campaign for a quick withdrawal.

"I think all I think he's trying to do is kick the can down the road and get UKIP off his back," he said.

Labour accused the Prime Minister of weakly following his party, rather than taking a decision in the best interests of the nation.

Lord Mandelson, the former Labour minister and EU trade commissioner, said David Cameron's plan for a fresh settlement with the EU will not be acceptable to leaders in Brussels.

"I think that many people, including many people in Brussels.. I think they will regard this speech as much more unvarnished, much more unqualified than they were expecting, but also unworkable," he said.